*THE POPULAR SCIENCE MONTHLY.*

MATHEMATICS IN EVOLUTION. |

WHILE we know that only Infinite Intelligence could reduce the entire phenomena of the universe to mathematical expression, it affords an observer constant surprise to find primitive laws of order and number recur again and again amid the infinite variety of Nature.

The spectroscope would seem to indicate that the elements of our present chemistry are really very complex structures, yet we find them, when grouped in all sorts of proportions as molecules, capable of crystallizing in forms of perfect geometrical symmetry, often of much simplicity. In botany, where the factors both chemically and mechanically are extremely various, we find simple laws obeyed in the disposition of leaves, flowers, and parts of flowers; a remarkable instance of which occurs in the growth of leaves on spirally-leaved plants. In the first order of them, a leaf is found in 12 the circumference of the stem, and throughout the series the arcs occupied by a leaf are respectively 13, 25, 38, 513, 821, and 1334, of a circle, the numerator and denominator of each fraction being those of the two next preceding added together.

In the highest plane of Nature, that of animal forms, the conditions fulfilled are too complex to permit any formulation of lines and angles, but natural history in its first chapters gives us the habitations of the nautilus and other organisms low in the scale of life, which in their beautiful volutes and spirals embody simple geometry. So also does the architecture of our common insects, the bee, wasp, and spider, which, wonderful as it is, must remain less so than the work of the microscopic coral zoöphytes, which, while severally living and building where it is easiest, yet unconsciously coöperate through successive generations to complete a structure of comparatively vast proportions and much symmetrical unity.

These few examples, which might be multiplied indefinitely, may serve as bases for the opinion that complex wholes, acting in many cases like simple ones, may be more easily reducible to mathematical treatment than might at first view be supposed, from the number and variety of ultimate factors concerned in any given problem. Nature would seem to act by but few first principles, which she constantly repeats in her various fields, and which, combined in different ways, yield all her infinite manifestations. The scientific progress of our times is marked by the continual absorption of diverse laws into higher and more general ones; thus the forms of force that used to be thought distinct entities are now proved to be interchangeable, and therefore essentially the same. A minor instance of a like kind occurs